Prove that: `3sin(pi/6)sec(pi/3)-4sin((5pi)/6)cot(pi/4)=1`

Explanation

To prove that \( 3\sin\left(\frac{\pi}{6}\right)\sec\left(\frac{\pi}{3}\right) - 4\sin\left(\frac{5\pi}{6}\right)\cot\left(\frac{\pi}{4}\right) = 1 \), we will start from the left-hand side (LHS) and simplify it step by step.

### Step 1: Substitute known values
We know the following trigonometric values:
- \( \sin\left(\frac{\pi}{6}\right) = \frac{1}{2} \)
- \( \sec\left(\frac{\pi}{3}\right) = 2 \)
- \( \sin\left(\frac{5\pi}{6}\right) = \sin\left(\pi - \frac{\pi}{6}\right) = \sin\left(\frac{\pi}{6}\right) = \frac{1}{2} \)
- \( \cot\left(\frac{\pi}{4}\right) = 1 \)
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